From our discussion in section (), it should be clear that almost all
results that have been derived in the literature regarding the finite size scaling relations
of \({\mathcal {L}}\)  (see, e.g., [1]} and references therein) will continue to remain valid for
the exponential of \((-{\mathcal {C}}_N)\) . Hence a separate analysis of the finite size behaviour of
\({\mathcal {C}}_N\)  is not necessary. For example, for both for large and small times,
\(\frac{\partial {\mathcal {C}}_N(t)}{\partial \lambda }\sim N~.\) 
